Question

The difference between two number is 2.Their product is 84 greater than the square of the smaller number the sum of the number is 164, 86, 84, 42

Answer 1

Let the 2 no.'s be a & b
Given:
a-b=2 .............(1)
and
ab=84+b^2
(b+2)*b=84+b^2............(since,a-b=2,a=b+2)
b^2+2b=84+b^2
2b=84
b=42
equation (1) implies
a-42=2
a=44
=> the 2 no.'s are 44 and42.
=> Hence, sum of 2 no.'s is 86.

Answer 2

Let the numbers be x and y and let y be the smaller number
Given that the difference = 2
⇒ x -y = 2
⇒ x = y+2  ------------(1)
Given that their product = 84 more than the square of the smaller no
⇒ xy = 84 +y²
⇒(y+2)y = 84 +y²
⇒ y² +2y = 84 +y²
⇒ y² -y² +2y = 84
⇒ 2y = 84
⇒  y =84/2
∴ y = 42
now, x = y+2
⇒x =42+2
∴ x =44
sum of them = x+y = 42+44 = 86